Starting from a holographic model a magnetic impurity interacting with a strongly coupled system, I focus on the challenges of computing gravitational backreaction in this model, which demands a study of the Israel junction conditions. I present general results on these junction conditions which may be relevant more generally in the AdS/boundary CFT correspondence. Furthermore, similar junction conditions for a bulk Chern-Simons field appearing in the holographic Kondo model are discussed. I then focus on the computation and interpretation of entanglement entropy in the holographic Kondo model. The holographic g-theorem will be discussed as well as a geometric construction that allows to reproduce results obtained by conformal perturbation theory on the boundary.